Question

Paul, Colin and Brian are waiters.

One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 1:3:5.
How much more does Brian get over Paul?

Answer 1

£34.40

Explanation:

Paul, Colin and Brian are waiters.

One night the restaurant earns tips totalling £77.40

They share the tips in the ratio 1:3:5

Paul gets
`(1)/(9)` × £77.40 = £8.60

Brian gets
`(5)/(9)` × £77.40 = £43.00

Brian gets £43.00 - £8.60 = £34.40 more than Paul.

Answer 2

whenever we have an amount to be divided in ratios, we simply divide the total amount by the sum of those ratios and then distribute accordingly. In this case, let's divide 77.40 by (1+3+5) and then distribute accordingly to each chap.

`\bf \stackrel{Paul}{1}~~:~~\stackrel{Colin}{3}~~:~~\stackrel{Brian}{5}~\hfill \cfrac{77.40}{1+3+5}\implies 8.6 \\\\\\ \stackrel{Paul}{1\cdot 8.6}~~:~~\stackrel{Colin}{3\cdot 8.6}~~:~~\stackrel{Brian}{5\cdot 8.6}\qquad \implies \qquad \stackrel{Paul}{8.6}~~:~~\stackrel{Colin}{25.8}~~:~~\stackrel{Brian}{43} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{Brian get this much more than Paul}}{43-8.6\implies 34.4}~\hfill`